Use the equation below to find the slope of the tangent line of the given function 𝑓(𝑥)= 2𝑥2+5𝑥 in terms of x.

Question

Use the equation below to find the slope of the tangent line of the given function 𝑓(𝑥)= 2𝑥2+5𝑥 in terms of x.

𝑚𝑡𝑎𝑛 = limΔ𝑥→0 Δy/Δx = limΔ𝑥→0 𝑓(𝑥+Δ𝑥)−𝑓(𝑥)/Δ𝑥

Answer 1

lim(f(x+Δx) - f(x))/Δx =

lim(2(x+Δx)² + 5(x+Δx) - 2x² - 5x)/Δx =

lim(2x² + 4xΔx + 2Δx² + 5x + 5Δx - 2x² - 5x)/Δx =

lim(4xΔx + 2Δx² + 5Δx)/Δx =

lim(4x + 2Δx + 5) =

4x + 5