Define for .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Define

h(x)=\dfrac{x^{2}-1}{x}

for

x\ne 0

. (i) Derive an expression for

h'(x)

and simplify it as far as possible. (ii) Determine all real numbers

x\ne 0

for which

h'(x)=0

. (iii) Using the sign of

h'(x)

, state whether

h

is increasing or decreasing on the intervals

(-\infty,-1)

(-1,0)

(0,1)

and

(1,\infty)