for the function ( f(x)=4 x^{2}-5 x ), evaluate and simplify.\n( \frac{f(x+h)-f(x)}{h}= )\nquestion help…

for the function ( f(x)=4 x^{2}-5 x ), evaluate and simplify.\n( \frac{f(x+h)-f(x)}{h}= )\nquestion help: message instructor\nsubmit question

for the function ( f(x)=4 x^{2}-5 x ), evaluate and simplify.\n( \frac{f(x+h)-f(x)}{h}= )\nquestion help: message instructor\nsubmit question

Answer

Explanation:

Step1: Find (f(x + h))

Substitute (x+h) into (f(x)): (f(x + h)=4(x + h)^{2}-5(x + h)) Expand ((x + h)^{2}): (f(x + h)=4(x^{2}+2xh+h^{2})-5x - 5h) (f(x + h)=4x^{2}+8xh+4h^{2}-5x - 5h)

Step2: Calculate (f(x + h)-f(x))

(f(x + h)-f(x)=(4x^{2}+8xh+4h^{2}-5x - 5h)-(4x^{2}-5x)) Remove the parentheses: (f(x + h)-f(x)=4x^{2}+8xh+4h^{2}-5x - 5h - 4x^{2}+5x) Simplify: (f(x + h)-f(x)=8xh+4h^{2}-5h)

Step3: Calculate (\frac{f(x + h)-f(x)}{h})

(\frac{f(x + h)-f(x)}{h}=\frac{8xh+4h^{2}-5h}{h}) Factor out (h) in the numerator: (\frac{f(x + h)-f(x)}{h}=\frac{h(8x + 4h-5)}{h}) Cancel out (h) ((h\neq0)): (\frac{f(x + h)-f(x)}{h}=8x + 4h-5)

Answer:

(8x + 4h-5)