Piecewise Function: Calculus

Question

Let f(x)={ k+4x, x≤−5

             { 7x² , x>−5

 

Find the constant k so that f is continuous at x=−5.

Answer 1

The right-sided limit of 7x² as x approaches -5 is 175.

 

The left-sided limit of k + 4x as x approaches -5 must also be 175, i.e. k -20 = 175 and k = 195

 

You should graph the 2 functions and make sure that f is continuous.  This is not a very satisfying problem in that the graph simply shows an intersection point similar to f(x) = |x| at x = 0.