What is the slope of the tangent to the curve y = 4x^3 - 3x^2 + 10 at the point (1, 11) ? ?

6

Explanation:

The slope of tangent to the curve is simply dy/dx of the curve.By differentiating the curve y w.r.t x we will get  the equation of the slope and after that we have to substitute the values of x and y in the new equation that is 1 and 11 respectively.

y=4x^3 - 3x^2 + 10

dy/dx = 12x^2 -6x                               (d(x^n)/dx=n.x^n-1)  

So substituting the values.

dy/dx= 12(1)^2 - 6(1)

=12-6

dy/dx = 6