If f(x)=(4x^2)-(8x)+3, find the gradient of y=f(x) at the point (0.5,0)
When you see the question asking you to find the gradient at a point in the curve, the first thing you have to do is differentiate. This is because when we differentiate, we find the equation of the tangent to the curve at that point, which is the same as the gradient. So for this equation, we can differentiate by using the main differentiation rule which is when y=xn, dy/dx=nxn-1. Using this we will get: dy/dx= f'(x) =(4x2)x(2-1)-(8x1)x(1-1)+(3x0)x(0-1) = 8x-8We then substitute in the point (0.5,0) where x=0.5 to get: f'(0.5)=-4The gradient at the point (0.5,0) is equal to -4.
