Question

find the slope of the tangent to the curve y=x*3-2x+1 at the point x=2​

Answer 1

we have to find the slope of tangent to the curve , y = x³ - 2x + 1 at the point x = 2

concept : we know, slope of tangent to the curve y = f(x) at point x = a is given by, dy/dx = f'(a)

here f'(a) is slope of tangent to the curve y = f(x) at point x = a.

y = x³ - 2x + 1

differentiating both sides,

dy/dx = d(x³ - 2x + 1)/dx = 3x² - 2

at x = 2 ⇒ dy/dx = 3(2)² -2 = 10

hence, slope of tangent to the curve at x = 2, is 10.