Find the coordinates of the points where the line y − 2x + 5 = 0 meets the curve 3x² − 4y² = 10 + xy
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Describe the nature of the stationary points of the function f(x) = 2x³ − 15x² + 24x, hence show them one the graph.
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Verify that x + 4 is not a factor of the polynomial function f(x) = 2x³ − 15x² + 24
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Sketch the graph of the rational function g(x) = 1/(4x – 8)
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A function is defined by the equation f(x) = mx² + nx + k. If f(2) = 7, f(0) = −3, and f(−1) = 2
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i) Determine the values of m, n, and k.
ii) Find the domain and range of f(x)
A function is defined by the equation f(x) = mx² + nx + k. If f(2) = 7, f(0) = −3, and f(−1) = 2
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The roots of the polynomial equation P(x) = x³ −7x² +Ax−8 form a geometric progression. Find,
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i) The roots of the polynomial equation
ii) The value of A
iii) The abscissa at the turning points on the curve
Find dy/dx in the following equation:
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yx² − y² + 5y − 20x = 14
Differentiate the function f(x) − 4x³ + 3x − 4 from first principles
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A 13 m long ladder leans against a wall. The bottom of the ladder is pulled away from the wall at the rate of 6 m/s. How fast does the heigh on the wall decrease when the foot of the ladder is 5 m away from the base of the wall?
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