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Show that x^2 - 8x +17 <0 for all real values of x

consider the discriminant b²-4ac 8²-4x1x17 64-68=-4 discriminant is below 0, there are no real roots therefore x² - 8x +17 <0

Answered by • Maths tutor

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Calculate the first derivative of f( x)= 3x^3+2x^2-5

f’(x)= 9x^3+4x

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The point P has coordinates (4, 5). The point Q has coordinates (a, b). A line perpendicular to PQ is given by the equation 5x+3y=11. Find an expression for b in terms of a.

First we should find the gradient of the line perpendicular to PQ by rearranging the equation.5x+3y=113y=11-5xy=11/5 -5/3xy= -5/3x + 11gradient is -5/3.We know that the gradients of perpendicular lines mu...

Answered by Staś B. • Maths tutor

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Let f(x) = 3x^4 - 8x^3 - 3. Find the x- values of the stationary points of this function.

Stationary points occur when f'(x) = 0. To find this, we differentiate f(x) to get f'(x) = 12x^3 - 24x^2. We know that at the stationary points are when f'(x) = 0. so we know that 12x^3 - 24x^2 = 0. We ca...

Answered by Yathavan S. • Maths tutor

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