The function is defined and continuous on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The function

h(x)=e^{x}-2x

is defined and continuous on the interval

[0,2]

. (i) Compute the average value of

h

[0,2]

. (ii) Show that the equation

h(c)=\bar h

has exactly one solution in

(0,2)

. Explain why no other solution can occur. (iii) Using a suitable numerical method, refine the value of

c

correct to three decimal places. Show all iterative steps used.