Consider the function f(x)=27x2 −16x,x≠0.Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100.[4]a.Use your graphic display calculator to find the equation of the tangent to the graph of y = f (x) at the point (–2, 38.75).Give your answer in the form y = mx + c.

To answer this question, we will follow these steps:

1. First, we need to sketch the graph of the function f(x) = 27x^2 - 16x for the given range of x and y. This can be done using a graphic display calculator or a graphing software. The graph will be a parabola opening upwards.

2. To find the equation of the tangent line at the point (-2, 38.75), we first need to find the derivative of the function f(x). The derivative of f(x) = 27x^2 - 16x is f'(x) = 54x - 16.

3. Evaluate the derivative at x = -2 to find the slope of the tangent line. f'(-2) = 54*(-2) - 16 = -108 - 16 = -124. So, the slope of the tangent line (m) is -124.

4. The equation of a line is given by y = mx + c. We know the slope (m) and a point on the line ((-2, 38.75)), so we can substitute these values into the equation to find the y-intercept (c). 38.75 = -124*(-2) + c. Solving for c gives c = 38.75 - 248 = -209.25.

5. Therefore, the equation of the tangent line to the graph of y = f(x) at the point (-2, 38.75) is y = -124x - 209.25.