Find the values of and such that the function | | condition | |---|---| | | | | | |…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Find the values of

b

and

c

such that the function

$f(x)$	condition
$x^2 - 1$	$\text{for } x \le 1$
$-x^2 + bx + c$	$\text{for } x > 1$

is both continuous and differentiable.

Related theory

Advanced Differentiation
Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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