Problem 4: Find the constant k such that the line y=43x+3 is tangent to the graph of the function f(x)=xk. Hint: A function and its tangent line share (at least) one point. Differentiate g(x)=x2c2x2+c2 where c is a constant. Find the second derivative of p(t)=t+32t2 f(x)=x3x1