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Question: For f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 }, is f differentiable at x = 1?Options: YesNoOnly ..
Question: The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?Options: YesNoOnly leftOnly ri..
Question: What is the minimum value of the function f(x) = 2x^2 - 8x + 10?Options: 2468Correct Answe..
Question: Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.Options..
Question: Determine the local maxima and minima of the function f(x) = x^3 - 6x^2 + 9x.Options: (0, ..
Question: Find the coordinates of the point on the curve y = x^3 - 3x + 2 where the tangent is horiz..
Question: For the function f(x) = 3x^3 - 12x^2 + 9, find the x-coordinates of the inflection points...
Question: Find the minimum value of the function f(x) = x^4 - 8x^2 + 16.Options: 0248Correct Answer:..
Question: What is the derivative of f(x) = x^2 + 2x + 1?Options: 2x + 22x + 1x + 22xCorrect Answer: ..
Question: Calculate ∫_1^e (ln(x))^2 dx.Options: 12ee^2Correct Answer: 2Solution: Using integration b..
Question: Evaluate ∫_0^π/2 sin^2(x) dx.Options: π/4π/2π/3π/6Correct Answer: π/4Solution: Using the i..
Question: Find the value of ∫_0^1 (x^4 + 2x^3 + x^2) dx.Options: 1/51/41/31/2Correct Answer: 1/4Solu..
Question: Evaluate ∫_0^1 (x^3 - 3x^2 + 3x - 1) dx.Options: 0123Correct Answer: 0Solution: The integr..
Question: Find the value of ∫_0^π sin(x) cos(x) dx.Options: 012πCorrect Answer: 0Solution: Using the..
Question: If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}..
Question: For the function f(x) = { x^2, x < 3; 9, x = 3; 3x, x > 3 } to be continuous at x = 3, the..
Question: The function f(x) = { 1/x, x ≠ 0; 0, x = 0 } is:Options: Continuous at x = 0Not continuous..
Question: If f(x) = x^3 - 3x + 2, then f(x) is continuous at:Options: All xx = 0x = 1x = -1Correct A..
Question: The function f(x) = { x^2, x < 2; 4, x = 2; 2x, x > 2 } is continuous at x = 2 if:Options:..
Question: Which of the following is a necessary condition for f(x) to be continuous at x = a?Options..
Question: The function f(x) = { 3x + 1, x < 1; 2x + 3, x >= 1 } is continuous at x = 1 if:Options: 3..
Question: If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x, x > 0 }, for f(x) to be continuous at x = 0, k m..
Question: The function f(x) = { x^2, x < 1; 2, x = 1; x + 1, x > 1 } is:Options: Continuous everywhe..
Question: Find the area under the curve y = x^4 from x = 0 to x = 1.Options: 1/51/41/31/2Correct Ans..
Question: The function f(x) = ln(x) + x has a minimum at:Options: x = 1x = 0x = ex = 2Correct Answer..
Question: The critical points of the function f(x) = x^3 - 6x^2 + 9x + 1 are:Options: x = 1, 3x = 0,..
Question: If the function f(x) = e^x + x^2 has a minimum at x = 0, then f(0) is:Options: 1023Correct..
Question: The slope of the tangent to the curve y = sin(x) at x = π/4 is:Options: 1√2/2√3/3√2Correct..
Question: For the function f(x) = 3x^3 - 12x^2 + 9x, the number of local maxima and minima is:Option..
Question: The maximum value of the function f(x) = -x^2 + 4x + 1 is:Options: 5976Correct Answer: 5So..
