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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The slope of a line tangent to the curve y = f(x) at the point where x = a is given by the value of f'(a).

For the curve defined by y = 4x^3 - 3x^2 + 10, the derivative `dy/dx` = 4*3*x^2 - 3*2*x = 12x^2 - 6x.

At the point where x = 1, `dy/dx` = 12 - 6 = 6

The slope of the tangent to the curve y = 4x^3 - 3x^2 + 10 at the point (1, 11) is 6.

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