sketch the graph of a function that satisfies the given conditions: [cont in description]

Question

f(0)=0

f is continuous and even

f'(x)=2x if 0<x<1

f'(x)=-1 if 1<x<3

f'(x)=1 if x>3

Answer 1

f(0)=0

f is continuous and even --- I assume this means symmetrical about the y axis

f'(x)=2x if 0<x<1 --- This means f(x) = x^2 (no constant of integration since we are given x(0) = 0

note that f(1) = 1

f'(x)=-1 if 1<x<3 --- Slope is -1, meaning the line goes from +1 to -1 over the interval x=1 to x=3 (f(3) = -1)

f'(x)=1 if x>3 --- The line continues with a +1 slope

Then, the mirror image for negative x