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The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)

First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can find ...
LP
Answered by Leon P. • Maths tutor
16428 Views

Let g (x) = 2x sin x . (a) Find g′(x) . (b) Find the gradient of the graph of g at x = π .

a) f'(x)=uv'+vu' if f(x)= uv u=2x u'=2 v=sin(x) v'=cos(x) g'(x)=2x cos(x) +2sin(x) b) g'(π) = 2π cos(π)+2sin(π) = 2 π (-1) + 2 (0) g'(π) = -2π
MB
Answered by Matias B. • Maths tutor
10827 Views

Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos 2 (x) - sin 2...
MP
10249 Views

For the equation y=2x+7, what is the gradient and the y intercept?

For all straight line equations as the one above, the equation is y=mx+c where: m is the gradient, c is the y-intercept. Thus from the arrangement of the given equation, gradient = 2 and y-intercept = 7 .
MP
21266 Views

What is 2/5 + 3/4 ?

2/5 = 8/20 3/4 = 15/20 8/20 + 15/20 = 23/20 23/20 = 1 and 3/20
KS
Answered by Kaya S. • Maths tutor
3167 Views