Question

Find (a) $f(x+h)$ (b) $f(x+h)-f(x)$ (c) $\frac{f(x+h)-f(x)}{h},$ where $h \neq 0,$ and (d) the value $\frac{f(x+h)-f(x)}{h}$ approaches as $h \rightarrow 0$ $$f(x)=2-x-x^{2}$$

          Find
(a) $f(x+h)$
(b) $f(x+h)-f(x)$
(c) $\frac{f(x+h)-f(x)}{h},$ where $h \neq 0,$ and
(d) the value $\frac{f(x+h)-f(x)}{h}$ approaches as $h \rightarrow 0$
$$f(x)=2-x-x^{2}$$

Added by Marc N.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Nicole Hoffman

06/09/2022

Step 1

Step 1: Find $f(x+h)$** Given $f(x) = 2 - x - x^2$, we substitute $x+h$ into the function: $$f(x+h) = 2 - (x+h) - (x+h)^2$$ $$f(x+h) = 2 - x - h - x^2 - 2xh - h^2$$ ** Show more…

Show all steps

Thanks for your feedback!

Find (a) $f(x+h)$ (b) $f(x+h)-f(x)$ (c) $\frac{f(x+h)-f(x)}{h},$ where $h \neq 0,$ and (d) the value $\frac{f(x+h)-f(x)}{h}$ approaches as $h \rightarrow 0$ $$f(x)=2-x-x^{2}$$