difference quotient\n$\frac{f(x + h)-f(x)}{h}$\n$f(x)=8x^{2}-9x$\n d) 16x + 8h - 9\n e) 16x - 1\n f) none of…
difference quotient\n$\frac{f(x + h)-f(x)}{h}$\n$f(x)=8x^{2}-9x$\n d) 16x + 8h - 9\n e) 16x - 1\n f) none of the above.
Answer
Explanation:
Step1: Find $f(x + h)$
Substitute $x+h$ into $f(x)=8x^{2}-9x$. $f(x + h)=8(x + h)^{2}-9(x + h)=8(x^{2}+2xh+h^{2})-9x - 9h=8x^{2}+16xh+8h^{2}-9x - 9h$
Step2: Calculate $f(x + h)-f(x)$
$f(x + h)-f(x)=(8x^{2}+16xh+8h^{2}-9x - 9h)-(8x^{2}-9x)$ $=8x^{2}+16xh+8h^{2}-9x - 9h - 8x^{2}+9x=16xh+8h^{2}-9h$
Step3: Calculate the difference - quotient
$\frac{f(x + h)-f(x)}{h}=\frac{16xh+8h^{2}-9h}{h}$ Factor out $h$ from the numerator: $\frac{h(16x + 8h-9)}{h}=16x + 8h-9$
Answer:
d. $16x + 8h-9$