Question

Sketch the graph of f(x) =x(1-x) over[0,1] . Refer to the graph and, without making any computations, find:

a. The average rate of change over [0,1]

b. The instantaneous rate of change at x=1/2

c. The values of days at which the rate of change is positive.

Can someone help me? I need step by step directions.

Answer 1

`f(x)=x(1-x)\\\\zeros:x=0\ and\ x=1\\\\vertex\ (x_v;\ y_v):\\\\x_v=(0+1)/(2)=(1)/(2)\\\\y_v=(1)/(2)(1-(1)/(2))=(1)/(2)*(1)/(2)=(1)/(4)`



`a)\\(f(0)-f(1))/(0-1)=0\\\\b)\\ROC_(inst)((1)/(2))=0\\\\c)\\(0;\ (1)/(2))`