Question

find a value for b so that f is a continuous function for all real numbers. Where f is defined
f(x){ x^2 + bx , for x < or = 5
{5sin(pi/2(x)) , for x >5

do i use deriviative here?

Answer 1

replace \(x\) by 5 in both expressions, set them equal and solve for \(b\)

no, you do not need derivatives

Answer 2

\[25+5b=5\sin(\frac{5\pi}{2})\] is a stsart

Answer 3

so would b = -4?

Answer 4

i think -5

Answer 5

25+5b = 5sin(pi/2(5))
25 + 5b = 5
5b = -20
b= -4?