Application of DerivativeHard
Question
Let f(x) = 
Equation of tangent line touching both branches of y = f(x) is
Equation of tangent line touching both branches of y = f(x) is
Options
A.y = 4x + 1
B.y = 4x + 4
C.y = x + 4
D.y = x + 1
Solution
Let y = mx + c be tangent touching both branches.
f(x) = - x2, y = mx + c , x < 0
x2 + mx + c = 0, m > 0 (∵ x < 0 ) (negative roots)
D = 0 ⇒ m2 = 4c
f(x) = x2 + 8, y = mx + c, x > 0
x2 - mx + 8 - c = 0, m > 0 (positive roots)
D = 0 ⇒ m2 = 32 - 4c
⇒ c = 4, m2 = 16 ⇒ c = 4, m = 4
f(x) = - x2, y = mx + c , x < 0
x2 + mx + c = 0, m > 0 (∵ x < 0 ) (negative roots)
D = 0 ⇒ m2 = 4c
f(x) = x2 + 8, y = mx + c, x > 0
x2 - mx + 8 - c = 0, m > 0 (positive roots)
D = 0 ⇒ m2 = 32 - 4c
⇒ c = 4, m2 = 16 ⇒ c = 4, m = 4
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