AP Calculus
posted by Anonymous .
Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0.
A. Does f have an inflection point at x=0? Explain your answer.
B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g. Write the equation of the tangent line to g at this point.
C. Use your tangent line to approximate g(0.3).
D. Find g''(0).

A yes, if f"=0 and f'≠0
B find g'(0)
Then the tangent line is
y5 = g'(0) (x0)
Respond to this Question
Similar Questions

Calculus (Global Max)
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first … 
Calculus
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first … 
Calculus
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first … 
Calculus
Suppose f is continuous on [0, 6] and satisfies the following x 0 3 5 6 f 1 4 1 3 f' 5 0 8 0 f" 1 3 DNE 3 x 0<x<3 3<x<5 5<x<6 f' +   f"   + (they are both tables) Identify the points of inflection a. There … 
CAlculus
The graph of the derivative, f '(x), is given. Determine the xcoordinates of all points of inflection of f(x), if any. (Assume that f(x) is defined and continuous everywhere in [3, 3]. If there are more answer blanks than inflection … 
Calculus answer check
A brand new stock is also called an initial public offering. This model predicts the percent overvaluation of a stock as R(t)=9t((t3)^3/2.718) where is the overvaluation in percent and t is the time in months after the initial issue. … 
Calculus
If f(x) is a continuous function with f"(x)=5x^2(2x1)^2(3x+1)^3 , find the set of values for x for which f(x) has an inflection point. A. {0,1/3,1/2} B. {1/3,1/2} C. {1/3} D. {1/2} E. No inflection points 
Calculus
Find the xcoordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x). I found the first and second derivative which … 
Differential Calculus
Determine all local extrema, concavity and inflection point/s for y = 2cos(x) in (0, 2Pi). Test by both First Derivative Test and Second Derivative Test and sketch the graph. 
Calculus
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 0. Which of the following statements is false?