Find the equation of the tangent to the curve y=3x^2-7x+5 at the point (2, 3) .
The starting point for a question like this is to differentiate the function - in this case the curve y=3x2 -7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested in the case where x=2 . When x=2, dy/dx = 6(2)-7 = 5 . We want to find the equation of the tangent in the form y=mx+c . We can substitute in the information we already have (known point from the question and the gradient which we have just calculated) . This gives 3=5(2)+c . Re-arranging this equation gives c=-7 . And so we can finish this solution with the statement "the equation of the tangent is y=5x-7".
