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Y= mX + c, 'X' is the horizontal value on the axis, the input value. The 'm' represents the gradient of the line, figured out by the change in y divided by the change in x. The 'c' value is the y intercep...

If you were to factorise this quadratic to find out its roots, you would get:

(x+1)(x+2)

which gives us roots of -1 and -2.

Remember that roots are where the graph crosses the x-axis,...

Use the product rule:

d/dx(fg) = f'g + fg'

f = x²    f' = 2x   g = sin(x)  g' = cos(x)

answer = 2xsin(x) + x²cos(x)

x² + 8x = (x + 4)² - 16, so x² + 8x - 5 = (x + 4)² - 16 - 5 = (x + 4)² - 21, so then (x + 4)² - 21 = 0 (x + 4)² = 21 -----> ...

As the tangent has the same gradient as the curve at the particular point, we need to find the gradient of the curve. To find the gradient we need to differentiate. Due to there being two variables in thi...