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(1.) f(x)=x^3+3x^2-2x+15. (a.) find the differential of f(x) (b.) hence find the gradient of f(x) when x=6 (c.) is f(x) increasing or decreasing at this point?

(1.) (a.) f’(x)=3x^2+6x-2 (b.) x=6 gradient=142 (c.) since f’(x)>0 at x=6, the function is increasing.
JE
Answered by Joel E. • Maths tutor
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The equation x^3 - 3*x + 1 = 0 has three real roots; Show that one of the roots lies between −2 and −1

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) + 1...
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Answered by Paul T. • Maths tutor
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Complete the square and find the roots (where y=0) of: "x^2+4x-5"

completing the square: (x+2)^2-9 finding the roots: (x+2)^2=9 x+2=+/-3 at y= 0, x= -5 or 1
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Answered by Liam Q. • Maths tutor
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y=4x^3+6x+3 so find dy/dx and d^2y/dx^2

dy/dx=12x^2+6 d^2y/dx^2=24x
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Answered by Swapnil P. • Maths tutor
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How useful are these sources for our understanding of Nazi Germany from 1933 to 1939? (32 mark)

There are many aspects which contribute to our understanding of Nazi Germany within the period of 33-39. Within source A we are prevented with a satirical cartoon which grates harshly upon the regime of the ...
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Answered by Kate M. • History tutor
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