Brief Calculus.

Question

Use the four step method to find the derivative of f (x) = 2x^3+4x-5

Answer 1

f(x) = 2x^3 -4x +5

f'(x) = 6x^2 -4

for ax^3 the derivative is 2ax^2, reduce the exponent by 1 and use the original exponent as a multiple of the coefficient

for 2x^3, the derivative is 2(3)x^2 = 6x^2

for -4x the derivative is just the coefficient

for 5 or any constant term the derivative = 0

add up the derivatives of each term: 6x^2 -4x +0

but you seem to be referring to the [f(x+h) - f(x)]/h method

where you take the limit as h approaches zero. See the other tutor's answer for that.

find f(x+h)

subtract f(x)

divide by h

take the limit as h goes to zero

Answer 2

Use the slider on x1 to see the tangent line at various points on f(x).

desmos.com/calculator/0c4u79yvif