Question

2

Using
f'(x) = instantaneous = lim f(x+h)-f(x).
rate of change
h→0
h
find f'(x) when f(x) = -4x² - 6x + 7

Answer 1

Step-by-step explanation

`\frac{ - 4(x + h)^(2) - 6(x + h) + 7 + 4 {x}^(2) + 6x - 7 }{h} \\ \frac{ - 4 {x}^(2) - 8hx - 4 {h}^(2) - 6x - 6h+ 7 + 4 {x}^(2) + 6x - 7 }{h} \\ \frac{ { - 4h}^(2) - 8hx - 6h }{h} \\ (h( - 4h - 8x - 6))/(h) \\ - 4h - 8x - 6 \\ since \: you \: given \: h \: approaches \: 0 \\ - 4(0) - 8x - 6 \\ -8x - 6`

Answer

-8x-6