Calculusderivatives
posted by Jake .
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
Respond to this Question
Similar Questions

Derivative Calculus
I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4  8/9x^9/8 + x^2  9x + 1 Answer: f’(x)= 15/4x^1/4  x ^1/8 + 2x 9 2) Let f(x)= 7x^3  9x. Find f’(5) Answer: f’(x)=21x^29 f’(5)=516 3) Find the given limit … 
Calculus (Derivatives)
What is the derivative of the this functon? 
ap calculus ab
for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) to compute the tangent line approximation of f(3). what does the difference between the actual value and the tangent line approximation have to do with the concavity (2nd … 
Calculusderivatives
Verify if these are correct answers. 1. The derivative of f(x)=e^2x e^2x is f'(x)=2e^2x  2e^2x? 
Calculus c
Let f be a twicedifferentiable function defined on the interval 1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the xaxis at … 
Calculus (derivatives)
Find the points on the graph of f where the tangent line is horizontal. x/x^2+25 I know you have to do the quotient rule to find the derivative, but then I do not know what to do after that. 
Calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For … 
Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = 2, g(4) = 6, g'(4) = 4, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: 27 b. Derivative of (f(x))/(g(x)) … 
Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = 2, g(4) = 6, g'(4) = 5, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: 27 b. Derivative of (f(x))/(g(x)) … 
calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, …