Consider the quadratic function

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

y = x^2

. The point

P(a, a^2)

lies on the function. The line

y = m(x - a) + c

also passes through P. What, if anything, can you say about the values of

m

and

c

? Suppose

y = m(x - a) + a^2

touches

y = x^2

at P. Find the value of

m