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+1 vote
1.5k views
in Derivatives by (49.2k points)
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If f(x) = \(\begin{cases} kx+5,when\;x\leq2 \\ x+1,when\;x>2 \end{cases}\) is continuous at x = 2 then k = ?

f(x) = (kx+5, when x ≤ 2), (x+1, when x > 2)

A. 2

B. -2

C. 3

D. -3

1 Answer

+2 votes
by (50.7k points)
selected by
 
Best answer

For continuity left hand limit must be equal to right hand limit and value at the point.

Continuous at x = 2.

⇒ 2+0+1

= 3

As f(x) is continuous

∴ 2k+5 = 3

K = -1.

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