Continuity And Differentiability
Sponsor Area
is equal to
Sponsor Area
equal to
-
does not exist
-
equal 
-
equal 
-
equal 
does not exist
equal
equal
equal
A.
does not exist
therefore does not exist
A function y = f(x) has a second order derivative f″(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is
-
(x-1)2
-
(x-1)3
-
(x+1)3
-
(x+1)2
B.
(x-1)3
f''(x) = 6(x - 1) f'(x) = 3(x - 1)2 + c ........ (i)
At the point (2, 1) the tangent to graph is y = 3x - 5 Slope of tangent = 3
∴ f'(2) = 3(2 - 1)2 + c = 3
3 + c = 3
⇒ c = 0
∴ From equation (i) f'(x) = 3(x - 1)2
f'(x) = 3(x - 1)2 f(x) = (x - 1)3 + k ...... (ii)
Since graph passes through (2, 1)
∴ 1 = (2 - 1)2 + k k = 0
∴ Equation of function is f(x) = (x - 1)3
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm3 /min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is
B.
Sponsor Area
Mock Test Series
Mock Test Series