# Study sets matching "ap calculus"

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Find the Zeros

Find the equation of the line tangent t…

Find the equation of the line normal to…

Show that f(x) is even.

f(x)=0

Get x and y.... Get the slope at x.... y-y1=m(x-x1)

negative reciprocal.

f(x)=f(-x)

Find the Zeros

f(x)=0

Find the equation of the line tangent t…

Get x and y.... Get the slope at x.... y-y1=m(x-x1)

Intermediate Value Theorem

Steps for using IVT

Mean Value Theorem

MVT steps

If f(x) is continuous on [a,b] and k is between f(a) and f(b)…

1) verify f(x) is continuous on given interval [a,b]... 2) find v…

If f(x) is continuous and differential on [a,b] then there mus…

1) verify that f(x) is continuous on interval and differential…

Intermediate Value Theorem

If f(x) is continuous on [a,b] and k is between f(a) and f(b)…

Steps for using IVT

1) verify f(x) is continuous on given interval [a,b]... 2) find v…

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

Intermediate Value Theorem

Mean Value Theorem

Power rule

Chain rule

If f is continuous, there exists a value c such that a<c<b and…

If f is continuous and differentiable, There exists a value c…

(x^n)'=nx^(n-1) where n≠0

(f(g(x))'=f'(g(x))g'(x)

Intermediate Value Theorem

If f is continuous, there exists a value c such that a<c<b and…

Mean Value Theorem

If f is continuous and differentiable, There exists a value c…

Extreme Value Theorem

The Mean Value Theorem for Derivatives

Rolle's Theorem

Fermat's Theorem

To find the absolute maximum and minimum values of a continuou…

If f is a differentiable function on the interval [a,b], there…

Let f be a function that satisfies the following 3 hypotheses:…

If f has a local maximum or minimum at c and if f'(c) exists,…

Extreme Value Theorem

To find the absolute maximum and minimum values of a continuou…

The Mean Value Theorem for Derivatives

If f is a differentiable function on the interval [a,b], there…

critical number

Relative max or min

A function is increasing when the first…

Point of Inflection

where f'(x)=0 or where f'(x)=DNR

Where f'(x)=0 or DNE and f'(x) changes sign

Positive, because y values are increasing

Where the second derivative changes sign. F"(x) can =0 or DNE

critical number

where f'(x)=0 or where f'(x)=DNR

Relative max or min

Where f'(x)=0 or DNE and f'(x) changes sign

Mean Value Theorem

Average Value

Fundamental Theorem of Calculus

Second Fundamental Theorem of Calculus

f'(c)=[f(b)-f(a)]/(b-a)

f(ave)= 1/(b-a)int(ab)f(x) dx

int(ab)f(x)dx= F(b)-F(a)

(d/dx)int[a(x)b(x)]f(t)dt= f[b(x)]b'(x)-f[a(x)]a'(x)

Mean Value Theorem

f'(c)=[f(b)-f(a)]/(b-a)

Average Value

f(ave)= 1/(b-a)int(ab)f(x) dx

Indeterminate Forms

Trick for: 0/0 and ∞/∞

Trick for: ∞*0

Trick for: ∞ - ∞

0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞, 0⁰, ∞⁰

Use L'Hopital directly

Rewrite as a division, then use L'Hopital

Find a common denominator then use L'Hopital

Indeterminate Forms

0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞, 0⁰, ∞⁰

Trick for: 0/0 and ∞/∞

Use L'Hopital directly

How is the area between two curves foun…

What is the disk method?

How is the area found between two curve…

How are limits of integration determine…

Subtract the lower curve( g(x) ) from the upper ( f(x) )... f(x)…

A method to find the volume of a revolving solid.... Imagine a s…

Same as x-axis where:... f(y) ≥ g(y)... however, it's not that we'…

1) The limits will be the 2 points in which they intersect. So…

How is the area between two curves foun…

Subtract the lower curve( g(x) ) from the upper ( f(x) )... f(x)…

What is the disk method?

A method to find the volume of a revolving solid.... Imagine a s…

Fundamental Theorem of Calculus

Mean Value Theorem (Formula)

Mean Value Theorem (Words)

Net Change Theorem

If f is continuous on the closed interval [a,b], then there ex…

The definite integral of the rate of change of a quantity F'(x…

Fundamental Theorem of Calculus

Mean Value Theorem (Formula)

If f is increasing what is f'?

What are your candidates for absolute e…

How do you find relative extrema of f?

Absolute Minimum

Positive

Relative extrema and endpoints

1. Set first derivative equal to 0, DNE... 2. Put values on a # l…

Lowest y-value in the entire graph

If f is increasing what is f'?

Positive

What are your candidates for absolute e…

Relative extrema and endpoints

Find the zeros

Show that f(x) is even

Show that f(x) is odd

Show that lim x→a f(x) exists

aka: find the roots... set function = 0... * factor or use quadratic…

Algebraically: show that f(-x)=f(x)... Graphically: see if symmet…

Algebraically: show that f(-x)= -f(x)... Graphically: see if symm…

Show that lim x→a- f(x) = lim x→a+ f(x)

Find the zeros

aka: find the roots... set function = 0... * factor or use quadratic…

Show that f(x) is even

Algebraically: show that f(-x)=f(x)... Graphically: see if symmet…

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Slope of secant line between two points, use to estimate insta…

Slope of tangent line at a point, value of derivative at a poi…

limit as h approaches 0 of [f(a+h)-f(a)]/h

Intermediate Value Theorem

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate insta…