Question

53) Consider the function f(x) whose second derivative is
f''(x)=7x+5sin(x). If f(0)=2 and f'(0)=4, what is f(3)f?

Answer #1

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Consider the function f(x) whose second derivative is
f''(x)=2x+5sin(x). If f(0)=3 and f'(0)=2, what is f(5)?

Consider the function f(x) whose second derivative is
f′′(x)=6x+10sin(x). If f(0)=2 and f′(0)=4, what is f(x)?

Consider the function f(x) whose second derivative is
f''(x)=2x+3sin(x). If f(0)=3 and f'(0)=4, what is f(5)

1. Consider the function f(x) whose second derivative is
f″(x)=10x+2sin(x). If f(0)=2 and f′(0)=3, what is f(x)?

Consider the function f ( x ) f ( x ) whose second derivative
is f ‘ ‘ ( x ) = 10 x + 7 sin ( x ) f ′ ′ ( x ) = 10 x + 7 sin ( x
) . If f ( 0 ) = 4 f ( 0 ) = 4 and f ‘ ( 0 ) = 3 f ′ ( 0 ) = 3 ,
what is f ( 2...

1)Consider the function f(x)f(x) whose second derivative is
f″(x)=9x+8sin(x). If f(0)=4 and f′(0)=2, what is f(5)?
2) Consider the function f(x)=(7/x^3)−(2/x^5).
Let F(x) be the antiderivative of f(x) with F(1)=0.
3)Given that the graph of f(x) passes through the point (5,4)
and that the slope of its tangent line at (x,f(x)) is 3x+3, what
is f(2)?
Then F(2) equals

1. Consider the function f(x) = 2x^2 - 7x + 9
a) Find the second-degree Taylor series for f(x) centered at x =
0. Show all work.
b) Find the second-degree Taylor series for f(x) centered at x =
1. Write it as a power series centered around x = 1, and then
distribute all terms. What do you notice?

1. Consider the function f(x) = x 3 + 7x + 2. (a) (10 pts) Show
that f has an inverse. (Hint: Is f increasing?) (b) (10 pts)
Determine the slope of the tangent line to f −1 at (10, 1). (Hint:
The derivative of the inverse function can be found using the chain
rule.)

question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

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