Question

show that the curve y = 6x^(3) + 5x - 3 has no tangent line with slope 4. How would I go about solving this?

Answer 1

the slope of any tangent line can be found by differentiating this function.
so differentiate it and equate the result to 4. then see if this gives any valid values for x. if not, then it implies that the curve has no tangent with a slope of 4.