Application of Derivatives
For x∈(0,25π), define f(x)=∫0xtsintdtThen f has : local maximum at π and 2π . local minimum at π and 2π local minimum at π and local maximum at 2π . local maximum at π and local minimum at 2π .
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If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.
Find the intervals in which the function f
given f(x)= s∈x+cosx, 0≤x ≤2π,
is strictly increasing or strictly decreasing.
For the curve y=4x3−2x5,find all the points at which the tangent passes through the origin.
A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.
Find the equation of the normal at the point (am2,am3)for the curve ay2=x3.
Find the maximum and minimum values, if any, of the following functions given by(i) f(x)=∣x+2∣−1 (ii) g(x)=−∣x+1∣+3 (iii) h(x)=sin(2x)+5 (iv) f(x)=∣sin4x+3∣
Prove that the following functions do not have maxima or minima:(i) f (x) = ex (ii) g(x)=logx(iii) h(x)=x3+x2+x+1
Find the maximum and minimum values of f , if any, of the function given by f(x)=∣x∣,x∈R.