How do you find f'(-1) using the limit definition given −5x2+8x+2?

The limit definition implies the formula f′(x)=limh→0f(x+h)−f(x)h.f′(x)=limh→0−5(x+h)2+8(x+h)+2−(−5x2+8x+2)hf′(x)=limh→0−5(x2+2xh+h2)+8x+8h+2+5x2−8x−2hf′(x)=limh→0−5x2−10xh−h2+8x−8x+2−2+8h+5x2hf′(x)=limh→0−10xh+8hhf′(x)=limh→0h(8−10x)hf'(x)=8-10xWe can evaluate through substitution.f'(-1)=8-10(-1)=18

Find out the answer to "How do you find f'(-1) using the limit..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Deangelo Hardy

Answered question

2022-04-16

How do you find f'(-1) using the limit definition given

- 5 x^{2} + 8 x + 2

Answer & Explanation

dabCrupedeedaejrg

Beginner2022-04-17Added 10 answers

The limit definition implies the formula

f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}

f^{'} (x) = lim_{h \to 0} \frac{- 5 {(x + h)}^{2} + 8 (x + h) + 2 - (- 5 x^{2} + 8 x + 2)}{h}

f^{'} (x) = lim_{h \to 0} \frac{- 5 (x^{2} + 2 x h + h^{2}) + 8 x + 8 h + 2 + 5 x^{2} - 8 x - 2}{h}

f^{'} (x) = lim_{h \to 0} \frac{- 5 x^{2} - 10 x h - h^{2} + 8 x - 8 x + 2 - 2 + 8 h + 5 x^{2}}{h}

f^{'} (x) = lim_{h \to 0} \frac{- 10 x h + 8 h}{h}

f^{'} (x) = lim_{h \to 0} \frac{h (8 - 10 x)}{h}

f'(x)=8-10x
We can evaluate through substitution.
f'(-1)=8-10(-1)=18

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?