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# Difference Quotient

+1
262
4
+322

Evaluate and Simplify.

f(x) = 2 + 4x − x^2,        f[(5 + h) − f(5)] / h

I got an answer but I am not sure if I am right or not.  My answer was, "4 - h"

Jan 16, 2019
edited by Ruublrr  Jan 17, 2019

#1
+533
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i have seen this before, i will show you.

also to everyone else who is confused about the operations, it is $$\frac{f(5 + h)-f(5)}{h}$$, not something else.

now, we have to calculate the numerator. f(h+5) is 2+4h+20-h^2-10h-25, and f(5) is -3. now you have (-h^2-6h)/h for the whole fraction, so the answer is -h-6.

someone check my work pleez

and hope this helped!

Jan 16, 2019
#4
+322
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I am doing the problem again and I found my mistake. Thank you.

Ruublrr  Jan 17, 2019
#2
+533
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ok here is my check: f(6)-f(5) should equal 3 according to you,

according to me it should be -7.

plugging in f(6), it is 2+24-36 or -10, and f(5) is 2+20-25 or -3, so it is -7 and i am right.

hope this helped, and the answer is actually -h-6.

Jan 16, 2019
#3
+106943
+3

Evaluate and Simplify.

f(x) = 2 + 4x − x^2,        f(5 + h) − f(5) / h

I got an answer but I am not sure if I am right or not.  My answer was, "4 - h"

$$\frac{f(5+h)-f(5)}{h}\\ =\frac{[2+4(5+h)-(5+h)^2]-[2+20-25]}{h}\\ =\frac{[2+20+4h-(25+h^2+10h)]-[-3]}{h}\\ =\frac{2+20+4h-25-h^2-10h+3}{h}\\ =\frac{4h-h^2-10h}{h}\\ =\frac{-h^2-6h}{h}\\ =\frac{h(-h-6)}{h}\qquad \text{where } h>0\\ =-h-6$$

So Asad, you were correct.   Good work!

Jan 16, 2019