Assignment:
Q1. Let f be a differentibale function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that.
I f'(c)=0
II f'(x)>0 when aIII f'(x)<0 when c
Which is true? Then tell why others false.
a. F'(c)=0
b. F"(c)=0
c. F(c) is an abs. max. value of f on [a,b].
d. F(c) is an abs. min. value of f on [a,b].
e. F(x) has a point of inflection at x=c.
Q2. A rectangle with one side on the x axis and one side on the line x=2 has its upper left vertex on the graph of y=x^2. For what value of x does the area of the rectangle attain its maximum vlaue? Explain.
(Figure is an x/y axis. The curve is y=x^2 and where the function goes approx. straight up almost verticle draw a line to the x axis. Then make a rectangle inside the curve and line to the x axis.)
Let f(x) = x^3 + x. If h is the inverse function of f then h'(20) equals? Answer is 1/4 but give step by step solution to get answer please.
Provide complete and step by step solution for the question and show calculations and use formulas.