6 short math problems
Then f′(5) is _____
and f′′(5) is ______
2.Use the chain rule to find the derivative of
You do not need to expand out your answer.
3.Use the chain rule to find the derivative of
Type your answer without fractional or negative exponents. Use sqrt(x) for x√.
4.Given the function g(x)=6x^3−9x^2−216x, find the first derivative, g′(x).
Notice that g′(x)=0 when x=−3, that is, g′(−3)=0.
Now, we want to know whether there is a local minimum or local maximum at x=−3, so we will use the second derivative test.
Find the second derivative, g"(x).
Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x=−3?
[Answer either up or down -- watch your spelling!!]
At x=−3 the graph of g(x) is concave _______
Based on the concavity of g(x) at x=−3, does this mean that there is a local minimum or local maximum at x=−3?
[Answer either minimum or maximum -- watch your spelling!!]
At x=−3 there is a local _________
5.The function f(x)=2x^3−39x^2+180x−10 has two critical numbers.
The smaller one is x =________
and the larger one is x = _________
6.The function f(x)=(5x+6)e^(−2x) has one critical number. Find it.
x = __________