Find the gradient of the curve with the equation y = x^3+7x^2+1 at x=2
The equation of the line is y=x3+7x2+1To find the equation for the gradient of the line, we need to differentiateDifferentiating gives us dy/dx = 3x2+14xWe can now find the gradient of the curve at any point, if we know the x co-ordinate at that pointWe want to find the gradient of the curve at x=2, so we put this into our equation for dy/dx3(2)2+14(2)=40so we know the gradient of the curve at x=2 is 40
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