Given fx x2 2 Use the definition of derivative to find f x

Given f(x) = x^2 + 2. Use the definition of derivative to find f\' (x)? Let f(x) = x^2 + 2x - 4. find the slope and equation of the tangent line to the curve at x = 2. Find the derivative of each function using the short cut rule for the following: f(x) = e^2x f(x) = ln5x f(x) = (2x + 5)(x^3-2x) f(x) = 2x^2 + 1/3x + 1 (2x^5 - 2x^2 + 100)^9 f(x) = 1/5x^5 - 1/x^2 + squareroot of x - 5x. Find the second and third derivative of (f).

Solution

f(x)= x² +2x-4

f\'(x)=2x+2

f\'(2)=2(2)+2=6

therefore the slope is 6.

f(x)=x²+2x-4

at x=2

f(2)=2²+2(2)-4=4

therefore the point is (2,4) and the slope is 6

And the slope point form is

y-y₁=m(x-x₁)

y-4=6(x-2)

y-4=6x-12

y= 6x-8

And that\'s the equation of tangent