Limit of a function; continuity; limit and continuity of sum, difference, product, quotient; L'Hopital's rule; continuity of composite functions; intermediate value property; derivatives — sum, difference, product, quotient, chain rule; derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions; tangents and normals; increasing and decreasing functions; derivatives of order two; maxima and minima; Rolle's and Lagrange's mean value theorems; derivatives of implicit functions up to order two.
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Q1 · Differential Calculus · MEDIUM
Let f : ℝ → ℝ be a differentiable function such that f(x + y) = f(x)f(y) for all x, y ∈ ℝ and f(0) = 1, f'(0) = 3. Then f(2) equals
Q2 · Differential Calculus · EASY
If y = x³ + 3x² - 9x + 7, then the function is strictly decreasing in the interval