Question

Find the derivative of f(x) = 2x2 + 7x at -3. That is, find f'(-3).

Answer 1

Answer:

Hello,

f'(-3) = -5

Step-by-step explanation:

f'(x) = 4 x + 7

f'(-3) = 4 (-3) + 7 = -12 + 7 = -5

or

f(-3) = 2 (-3)² + 7 (-3) = 18 - 21 = -3

f(-3 + h) = 2 (-3 + h)² + 7 (-3 + h)

= 2 (9 - 6h + h²) - 21 + 7h

= 18 - 12h + 2h²  - 21 + 7h

= 2h² - 5h - 3

( f(-3 + h) - f(-3) ) / h = 2h - 5

f'(-3) = lim h→0 ( f(-3 + h) - f(-3) ) / h = lim h→0 (2h - 5) = -5