Application of Derivatives
How many real solutions does the equation x7+14x5+16x3+30x560=0have?
Find the equation of tangent and normal to the curve x=(1+t2)2at2,y=(1+t2)2at3 at the point for which t=21˙
Water is dropped at the rate of 2 m3/s into a cone of semi-vertical angle is 45∘ . If the rate at which periphery of water surface changes when the height of the water in the cone is 2m is d. Then the value of 5d is _____ m/sec
Let f:[2,7]0,∞ be a continuous and differentiable function. Then show that (f(7)−f(2))3(f(7))2+(f(2))2+f(2)f(7)=5f2(c)fprime(c), where c∈[2,7]˙
If fogoh(x) is an increasing function, then which of the following is not possible? (a)f(x),g(x),andh(x) are increasing (b)f(x)andg(x) are decreasing and h(x) is increasing (c)f(x),g(x),andh(x) are decreasing