determine the values of x such that y=x^2 and y=1/x have the same slope

Question

only allowed to use the first principles definition for a derivative 😕

Answer 1

I take it that you cannot use the power rule.

Using the definition of derivative: for d/dx(x²) Lim as h→0 ((x+h)²-x²)/h = Lim as h→0 (2x+h) = 2x

d/dx (1/x) = Lim as h→0 (1/(x+h) - 1/x))/h = Lim as h→0 (1/h) (x-(x+h))/(x(x+h)) =Lim as h→0 -1/(x² +hx) = -1/x²

now just equate the derivative expressions and solve for x values.

Please consider a tutor. Take care.