Let fx 2ex 3x2 whose graph is given to the right Sketch i

Let f(x) = 2ex - 3x2 , whose graph is given to the right. Sketch in the tangent lines to f (x) at x = l,x = 2, and x = 3. and calculate their slopes.

Solution

f\'(x) = 2e^x - 3*(5/2)xx

Slope at x = 1

f \' (1) = 2e - 15/2 = -2.08

f \'(2) = 2e² - 3*(5/2) 2*2 = -6.54

f \' (3) = 2e³ - 3*(5/2) 3*3 = 0.834