Brief Calculus.

Question

A. Use the Four Step Method to find the derivative of 𝑓(𝑥)=5𝑥^2−3𝑥+2

B. Find the equation of the line that is tangent to f(x) at x=5

Answer 1

that's the point (5, 5(5^2) - 3(5)+2 = (5, 112)

slope = 10x-3 = 10(5)

= 50-3 = 47 = m

m= 47 = (y-112)/(x-5)

y-112 = 47x - 235

y= 47x -235 +112

y=47 - 123

Answer 2

1: f(x+h) = 5(x+h)²-3(x+h)+2 = 5x²-10xh+5h² -3x -3h +2

2: f(x+h)-f(x) = 5x²+10xh+5h² -3x-3h+2 -(5x²-3x+2) = 10xh+5h²-3h

3: (f(x+h)-f(x))/h = 10x+5h-3

4: f '(x) = lim h→0 10x+5h-3 = 10x-3

f'(5) = 10(5)-3 = 47 = m

f(5) = 5(5)²-3(5)+2 = 125-15+2 = 112 --> (5, 112)

y-y₀ = m(x-x₀₎

y-112=47(x-5)

y = 47x-235+112

y= 47x-123