Application of Derivatives
Find the slope of the tangent to the curve y=3x4−4xat x=4.
If the curve y=ax2−6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=23, then find the values of aandb˙
Does there exists line/lines which is/are tangent to the curve y=sinxat(x1,y1) and normal to the curve at (x2,y2)?
Let f be differentiable for all x, If f(1)=−2andfprime(x)≥2 for all x∈[1,6], then find the range of values of f(6)˙
Statement 1: If f(x) is differentiable in [0,1] such that f(0)=f(1)=0, then for any λ∈R, there exists c such that fprime(c)=λf(c),0<c<1. statement 2: if g(x) is differentiable in [0,1], where g(0)=g(1), then there exists c such that gprime(c)=0,
In an acute triangle ABC if sides a,b are constants and the base angles AandB vary, then show that a2−b2sin2AdA=b2−a2sin2BdB
Two men PandQ start with velocity u at the same time from the junction of two roads inclined at 450 to each other. If they travel by different roads, find the rate at which they are being separated.