Use the formula f'(x) = lim f(z)-f(x) z-x to find the derivative of the following function....

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Use the formula f'(x) = lim f(z)-f(x) z-x to find the derivative of the following function. f(x)=2+x f'(x)= (Type an exact answer, using radicals as needed.) Compute the right-hand and left-hand derivatives as limits and check whether the function is differentiable at the point P. y-f(x) y=3x-21 Select the correct choice below and fill in the answer boxes within your choice. (Type integers or simplified fractions.) OA. The given function is not differentiable at the point P. The right-hand and the left-hand derivative of derivative of the given function is the given function is y=x+3 P(9.6) B. The given function is differentiable at the point P. The right-hand derivative of the given function is the given function is and the left-hand derivative of Determine if the following piecewise-defined function is differentiable at x=0. 2x-2, x0 f(x)= x+4x-2. x <0 Select the correct choice below and, if necessary, fill in the answer boxes within your choice. O A. The function is not differentiable at x=0 because it is continuous at x=0 and lim f(0+ h) -f(0) h f(0+h)-f(0) and lim h _0+4 B. (Type integers or simplified fractions.) The function is differentiable at x=0 because it is continuous at x=0 and lim f(0+ h) -f(0) h (Type integers or simplified fractions.) 0+4 OC. The function is not differentiable at x=0 because it is not continuous at x=0. +0+4 f(0+h) -f(0) and lim .0+4 h Use the formula f'(x) = lim f(z)-f(x) z-x to find the derivative of the following function. f(x)=2+x f'(x)= (Type an exact answer, using radicals as needed.) Compute the right-hand and left-hand derivatives as limits and check whether the function is differentiable at the point P. y-f(x) y=3x-21 Select the correct choice below and fill in the answer boxes within your choice. (Type integers or simplified fractions.) OA. The given function is not differentiable at the point P. The right-hand and the left-hand derivative of derivative of the given function is the given function is y=x+3 P(9.6) B. The given function is differentiable at the point P. The right-hand derivative of the given function is the given function is and the left-hand derivative of Determine if the following piecewise-defined function is differentiable at x=0. 2x-2, x0 f(x)= x+4x-2. x <0 Select the correct choice below and, if necessary, fill in the answer boxes within your choice. O A. The function is not differentiable at x=0 because it is continuous at x=0 and lim f(0+ h) -f(0) h f(0+h)-f(0) and lim h _0+4 B. (Type integers or simplified fractions.) The function is differentiable at x=0 because it is continuous at x=0 and lim f(0+ h) -f(0) h (Type integers or simplified fractions.) 0+4 OC. The function is not differentiable at x=0 because it is not continuous at x=0. +0+4 f(0+h) -f(0) and lim .0+4 h