For The Function F ( X ) = − 5x^2 − 2x , Evaluate And Fully Simplify ...

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login Calculus Precalculus For the function f ( x ) = − 5x^2 − 2x , evaluate and fully simplify each of the following

For the function f ( x ) = − 5x^2 − 2x , evaluate and fully simplify each of the following

f(x+h)=

f(x+h)−f(x)/h=

Follow • 2 Add comment More Report

3 Answers By Expert Tutors

Best Newest Oldest By: Best Newest Oldest

Firstly, you want to identify f(x+h). Back in algebra 2, we learned that f(x+h) means we add h to every x in our function.

f(x)= -5x2 - 2x

f(x+h) = -5(x+h)2 -2(x+h)

Now our difference quotient is (f(x+h)-f(x))/(h). Previously we found f(x+h), and we know f(x), so lets plug it in.

[f(x+h)-f(x)] / (h) = [-5(x+h)2 -2(x+h) - (-5x2- 2x)] / h

Lets simplify:

1. -5(x+h)2 = -5(x+h)(x+h) = -5(x2 +2xh+h2) = -5x2- 10xh- 5h2
2. -2(x+h) = -2x - 2h

So that,

[f(x+h)-f(x)] / (h) = [-5x2- 10xh- 5h2 - 2x - 2h - (-5x2- 2x)] / (h) FOIL and Distribute -2

= [-5x2- 10xh- 5h2 - 2x - 2h + 5x2+2x] / (h) Distribute the negitive

= [- 10xh - 5h2 - 2h ] / (h) Add like terms to cancel out terms that do not contain an h

= [h(- 10x-5h-2)] / (h) Factor out an h

= - 10x-5h-2 Simplify

The difference quiotent for f(x)=-5x2-2 is [f(x+h)-f(x)]/(h) = -10x-5h-2

If anything is incorrect, please let me know and I will promptly correct it. :)

Upvote • 0 Downvote Add comment More Report

f(x+h) = -5(x+h)2-2(x+h) = -5(x2+2xh+h2)-2x-2h = -5x2-10xh-5h2-2x-2h

f(x+h)-f(x) = -5x2-10xh-5h2-2x-2h +5x2+2x = -10xh-5h2-2h

(f(x+h)-f(x))/h = -10x-5h-2

Upvote • 0 Downvote Add comment More Report f ( x ) = − 5x^2 − 2xf ( x+h ) = − 5(x+h)^2 − 2(x+h)

(f ( x+h )-f(x))/h=(− 5(x+h)^2 − 2(x+h)-(− 5x^2 − 2x))/h

= (-5x^2-10xh-5h^2-2x-2h+5x^2+2x)/h

=(-10xh-5h^2-2h)/h=-10x-5h-2

Upvote • 0 Downvote Add comment More Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem. Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » < > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

RELATED TOPICS

Math Algebra 1 Algebra 2 Trigonometry Algebra Pre Calculus Limits Functions Math Help Pre Calculus ... Derivative Precalculus Homework Ap Calc Ap Calculus Calc Integration Derivatives Calculus 3 Calculus 2 Calculus 1

RELATED QUESTIONS

CAN I SUBMIT A MATH EQUATION I'M HAVING PROBLEMS WITH?

Answers · 3

If i have rational function and it has a numerator that can be factored and the denominator is already factored out would I simplify by factoring the numerator?

Answers · 7

how do i find where a function is discontinuous if the bottom part of the function has been factored out?

Answers · 3

find the limit as it approaches -3 in the equation (6x+9)/x^4+6x^3+9x^2

Answers · 8

prove addition form for coshx

Answers · 4

RECOMMENDED TUTORS

Whitney T.

5 (351)

Sean M.

5.0 (1,173)

Abigail C.

5.0 (5,209) See more tutors

find an online tutor

• Calculus tutors
• Precalculus tutors
• Multivariable Calculus tutors
• Differential Equations tutors
• AP Calculus tutors
• College Algebra tutors
• Algebra 2 tutors
• AP Calculus AB tutors