Simplify the difference quotient f(x+h) - f(x) all over h. Please show work.

(1) y= square root of x

(2) y= 40x-16x^2

Y= √x

f(x+h) =√(x+h)

f(x+h)-f(x) =√(x+h)- √x

[f(x+h)-f(x)]/h =(√(x+h)- √x)( √(x+h)+ √x)/[h(√(x+h)+ √x]

= (x+h-x)/h *1/(√(x+h)+ √x]

= (h)/h *1/(√(x+h)+ √x]

= 1/(√(x+h)+ √x]

(2) y =40x-16x^{2}

f(x+h) = 40(x+h) -16(x+h)^{2}

f(x+h)-f(x) = 40 x+4oh -40x -16(x^{2}+2xh+h^{2}-x^{2})

= 40h -16(2xh+h^{2})

[f(x+h)-f(x)]/h = 40 -32x-16h

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up