Calculusderivatives
posted by Jake on .
Verify these answers~
1. For what value(s) of x does f(x)=(x^216)^5 have a horizontal tangent?
a) x=4,4
b) x=4,0,4
c) x=0
d) x=0,4
Answer is B, x=4,0,4

2. What is the derivative of f(x)=(3x^2+7)^3?
a) f'(x)=3(3x^2+7)^2
b) f'(x)=18(3x^2+7)^2
c) f'(x)=18x(3x^2+7)^2
d) f'(x)=3(3x^2+7)^2
Answer: C

3. What is the yintercept of the line that is tangent to f(x)=4/(3x+1) at (1,2)?
a) 5
b) 3/4
c) 3/4
d) 2
Answer: B

4. For which point(s) on the graph of f(x)=5x/(x+2) is the slope of the tangent 2/5?
a) (3,15)
b) (7, 35/9)
c) (3,3) and (7,,7)
d) (24, 60/13)
Answer is C


I am only going to do one of them. That should give you the idea.
1. For what value(s) of x does f(x)=(x^216)^5 have a horizontal tangent?

when is dy/dx = 0?
dy/dx = 5 (x^216)(2x)
when is that zero
When x = 0 obviously but also when
x^2 = 16
that is when x = 4 or x = 4
so
4 , 0 , +4
a) x=4,4
b) x=4,0,4
c) x=0
d) x=0,4
Answer is B, x=4,0,4