Point A lies on the curve y=3x^2+5x+2. The x-coordinate of A is 2. Find the equation of the tangent to the curve at the point A
First differentiate the function with respect to x, dy/dx=6x+5 this finds the gradient function now calculate the gradient at point A by inputing x=2 into the gradient function 6(2)+5=17. Now using y=mx+c where m is known gives y=17x+c now must solve for c, at x=2 y=24 by 3(2)^2+5(2)+2=24 now we can solve for c where 24=17(2)+c this gives c=-10 y=17x-10
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