Functions, derivatives, and critical numbers
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Find f(x), given that...
Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.
Find the critical numbers...
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Solution Summary
This shows how to find a function from the derivative and the graph of the derivative, as well as finding critical numbers and extrema.
Solution Preview
Please see the attached file for answers. Thanks.
1. Find f(x), given that
for all x and
Answer:
First integrate the expression using the power rule and trig identities. (hint: the derivative of the sin function is the cosine function)
f(x) = 10x2 + 3 sin(x)+ C
Now plug in f(0) = 2 and solve for C
f(0) = 10(0)2 + 3 sin(0)+ C = 2
0 + 0 + C = 2
C = 2
So the total equation now becomes
f(x) = 10x2 + 3 sin(x)+ 2
2. Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.
Answer:
We can look at the graph and see it is ...
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