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
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
If (1 + 3 + 5 + ...+ a) + (1 + 3 + 5 + ...+ b) = (1 + 3 + 5 + ...+ c), where each set of paren theses contains the sum o...The length of the subtangent at any point of the curve y = ax3 is-...If α be the angle of intersection between the curves y = ax and y = bx, then tanα is equal to-...For the parabola y2 = 4ax, the ratio of the subtangent to the abscissa is -...The side of a square is increasing at the rate of 0.2 cm/sec, then the rate of increase of the perimetre of the square i...