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Find the equation of the tangent to the curve y=3x^2-7x+5 at the point (2, 3) .

The starting point for a question like this is to differentiate the function - in this case the curve y=3x²-7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested i...

Answered by Matthew S. • Maths tutor

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Find the equation of the line perpendicular to the line y= 3x + 5 that passes through the point (-1,4)

Logically work through the problem: 1) Plot all the information that is available so you can visualise the problem better (always encouraged for graphical questions) 2) Understand that the gradient of the...

Answered by Chagall C. • Maths tutor

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Given the function f(x)=λx^3 + 9, for λ other than zero, find the inflection point of the graph in terms of λ. How does the slope of the line tangent to the inflection point changes as λ varies from 0 to 1?

f'(x) = 3λx^2f''(x) = 6λxFor the inflection point (x₀,y₀), it is true that f''(x₀)=0 so 6λx_o=0 => x₀= 0 (since λ cannot be zero)Therefore, the inf...

Answered by Claire D. • Maths tutor

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By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.

cos(2x)=cos²(x)-sin²(x)=2cos²(x)-1
Therefore:cos(2x)/cos²(x)=(2cos²(x)-1)/cos²(x)=2cos²(x)/cos²(x) - 1/cos

Answered by Hugo F. • Maths tutor

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How do I differentiate an expression of the form y = (ax+b)^n?

In order to differentiate this we need to use the chain rule- first let u = ax + b. Then differentiating, du/dx = a. By substituting into the original expression, we can obtain y = u^n. Differentiating th...

Answered by Sam C. • Maths tutor

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