The correct statement is (A) f(c) is an extreme value of `f(x)` if `f prime(c)=0`

True or False statements: If a function f has an extreme point at x = c, then f' (c ) = 0

True or False statements: If a function f is twice differentiable at x = c,f' (c ) = 0 and f" (c ) > 0, then f has a local minimam value at x = c.

The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime)(x^2) for all real xdot Given that f(1)=1 and f^(1)=8 , then the value of f^(prime)(1)+f^(1) is 2 b. 4 c. 6 d. 8

The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime)(x^2) for all real xdot Given that f(1)=1 and f^(1)=8 , then the value of f^(prime)(1)+f^(1) is 2 b. 4 c. 6 d. 8

if f(x)=mx+c and f(0)=f'(0)=1 then find the value of f(3)

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .

Statement 1: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi) Statement 2: For f(x)=sinx ,f(pi)=f(3pi)dot a. Statement 1 and Statement 2, both are correct and Statement 2 is the correct explanation for Statement 1 b. Statement 1 and Statement 2, both are correct and Statement 2 is not the correct explanation for Statement 1 c. Statement 1 is correct but Statement 2 is wrong. d. Statement 2 is correct but Statement 1 is wrong.

If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x) for which F(c) is a maximum, f^(prime)(c) is given by a. f^(prime)(c)=(f(b)-f(a))/(b-1) b. \ f^(prime)(c)=(f(b)-f(a))/(a-b) c. f^(prime)(c)=(2(f(b)-f(a)))/(b-a) d. f^(prime)(c)=0

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that (a) f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c) (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that f^(prime)(c)=0 (b) f^(prime)(c)>0 f^(prime)(c)<0 (d) none of these